

FOLLOWUS
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
School of Science, Chongqing University of Posts and Telecommunications, Chongqing 430065, China
NAAM-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Jun MA, E-mail: hyperchaos@163.com; hyperchaos@lut.edu.cn
Received:09 November 2019,
Revised:2020-;3-31,
Published Online:21 April 2020,
Published:2020-09
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Yong LIU, Wan-jiang XU, Jun MA, et al. A new photosensitive neuron model and its dynamics[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1387-1396.
Yong LIU, Wan-jiang XU, Jun MA, et al. A new photosensitive neuron model and its dynamics[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1387-1396. DOI: 10.1631/FITEE.1900606.
生物神经元可感知多种外界刺激信号,这些信号可被转化为等效的电流来驱动神经元。因此,神经元的膜电位可通过外刺激调控呈现各类放电模式。实际上,可靠的神经元模型应考虑内在的生物物理效应以及功能性编码。一个重要且有趣的问题是弄清外界信号转录过程的物理机制。外界信号通常被转化为等效的跨膜电流或信号源以诱发动作电位。提出一个光电神经元模型以表达其非线性编码过程和外界光信号驱动神经元的电活动响应。在该模型中,使用一个光电管激活一个简单的FitzHugh-Nagumo(FHN)神经元电路,并施加外界光信号(光照)于光电管产生时变电流源或电压源以驱动神经元电路。这种光电管耦合的神经元电路能探测和感知外界光信号,其作用类似于人工电子眼。通过分岔详细分析神经元模态迁移和放电斑图特征。通过调制神经元电路的光电流,神经元膜电位序列可呈现静息态、尖峰放电、簇放电和混沌特征。这些结果可为进一步研究神经动力学和神经电路提供参考。
Biological neurons can receive inputs and capture a variety of external stimuli
which can be encoded and transmitted as different electric signals. Thus
the membrane potential is adjusted to activate the appropriate firing modes. Indeed
reliable neuron models should take intrinsic biophysical effects and functional encoding into consideration. One fascinating and important question is the physical mechanism for the transcription of external signals. External signals can be transmitted as a transmembrane current or a signal voltage for generating action potentials. We present a photosensitive neuron model to estimate the nonlinear encoding and responses of neurons driven by external optical signals. In the model
a photocell (phototube) is used to activate a simple FitzHugh-Nagumo (FHN) neuron
and then external optical signals (illumination) are imposed to excite the photocell for generating a time-varying current/voltage source. The photocell-coupled FHN neuron can therefore capture and encode external optical signals
similar to artificial eyes. We also present detailed bifurcation analysis for estimating the mode transition and firing pattern selection of neuronal electrical activities. The sampled time series can reproduce the main characteristics of biological neurons (quiescent
spiking
bursting
and even chaotic behaviors) by activating the photocell in the neural circuit. These results could be helpful in giving possible guidance for studying neurodynamics and applying neural circuits to detect optical signals.
P Agostini , , , G Petite . . Photoelectric effect under strong irradiation . . Contemp Phys , , 1988 . . 29 ( ( 1 ): ): 57 - - 77 . . DOI: 10.1080/00107518808213751 http://doi.org/10.1080/00107518808213751 . .
B Bao , , , Q Yang , , , L Zhu , , , 等 . . Chaotic bursting dynamics and coexisting multistable firing patterns in 3D autonomous Morris-Lecar model and microcontroller-based validations . . Int J Bifurc Chaos , , 2019 . . 29 ( ( 10 ): ): 1950134 DOI: 10.1142/S0218127419501347 http://doi.org/10.1142/S0218127419501347 . .
H Bao , , , N Wang , , , HG Wu , , , 等 . . Bi-stability in an improved memristor-based third-order Wien-bridge oscillator . . IETE Techn Rev , , 2019 . . 36 ( ( 2 ): ): 109 - - 116 . . DOI: 10.1080/02564602.2017.1422395 http://doi.org/10.1080/02564602.2017.1422395 . .
CAS Batista , , , RL Viana , , , FAS Ferrari , , , 等 . . Control of bursting synchronization in networks of Hodgkin-Huxley-type neurons with chemical synapses . . Phys Rev E , , 2013 . . 87 ( ( 4 ): ): 042713 DOI: 10.1103/PhysRevE.87.042713 http://doi.org/10.1103/PhysRevE.87.042713 . .
BK Bera , , , D Ghosh , , , M Lakshmanan . . Chimera states in bursting neurons . . Phys Rev E , , 2016 . . 93 ( ( 1 ): ): 012205 DOI: 10.1103/PhysRevE.93.012205 http://doi.org/10.1103/PhysRevE.93.012205 . .
BK Bera , , , S Rakshit , , , D Ghosh , , , 等 . . Spike chimera states and firing regularities in neuronal hypernetworks . . Chaos , , 2019 . . 29 ( ( 5 ): ): 053115 DOI: 10.1063/1.5088833 http://doi.org/10.1063/1.5088833 . .
S Binczak , , , S Jacquir , , , JM Bilbault , , , 等 . . Experimental study of electrical FitzHugh-Nagumo neurons with mod-ified excitability . . Neur Networks , , 2006 . . 19 ( ( 5 ): ): 684 - - 693 . . DOI: 10.1016/j.neunet.2005.07.011 http://doi.org/10.1016/j.neunet.2005.07.011 . .
D Brust . . Band-theoretic model for the photoelectric effect in silicon . . Phys Rev , , 1965 . . 139 ( ( 2A ): ): A489 DOI: 10.1103/PhysRev.139.A489 http://doi.org/10.1103/PhysRev.139.A489 . .
D Cubero , , , JP Baltanás , , , J Casado-Pascual . . High-frequency effects in the FitzHugh-Nagumo neuron model . . Phys Rev E , , 2006 . . 73 ( ( 6 ): ): 061102d DOI: 10.1103/PhysRevE.73.061102 http://doi.org/10.1103/PhysRevE.73.061102 . .
LX Duan , , , QY Cao , , , ZJ Wang , , , 等 . . Dynamics of neurons in the pre-B?tzinger complex under magnetic flow effect . . Nonl Dynam , , 2018 . . 94 ( ( 3 ): ): 1961 - - 1971 . . DOI: 10.1007/s11071-018-4468-7 http://doi.org/10.1007/s11071-018-4468-7 . .
V Erokhin , , , T Berzina , , , P Camorani , , , 等 . . Material memristive device circuits with synaptic plasticity: learning and memory . . BioNanoScience , , 2011 . . 1 ( ( 1-2 ): ): 24 - - 30 . . DOI: 10.1007/s12668-011-0004-7 http://doi.org/10.1007/s12668-011-0004-7 . .
AS Etémé , , , CB Tabi , , , A Mohamadou , , , 等 . . Elimination of spiral waves in a two-dimensional Hindmarsh-Rose neural network under long-range interaction effect and frequency excitation . . Phys A , , 2019 . . 533 122037 DOI: 10.1016/j.physa.2019.122037 http://doi.org/10.1016/j.physa.2019.122037 . .
R Fitzhugh . . Impulses and physiological states in theo-retical models of nerve membrane . . Biophys J , , 1961 . . 1 ( ( 6 ): ): 445 - - 466 . . DOI: 10.1016/S0006-3495(61)86902-6 http://doi.org/10.1016/S0006-3495(61)86902-6 . .
VA Gaiko . . Multiple limit cycle bifurcations of the FitzHugh-Nagumo neuronal model . . Nonl Anal Theory Methods Appl , , 2011 . . 74 ( ( 18 ): ): 7532 - - 7542 . . DOI: 10.1016/j.na.2011.08.017 http://doi.org/10.1016/j.na.2011.08.017 . .
MY Ge , , , Y Jia , , , Y Xu , , , 等 . . Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation . . Nonl Dynam , , 2018 . . 91 ( ( 1 ): ): 515 - - 523 . . DOI: 10.1007/s11071-017-3886-2 http://doi.org/10.1007/s11071-017-3886-2 . .
AT Georges . . Theory of the multiphoton photoelectric effect: a stepwise excitation process . . Phys Rev B , , 1995 . . 51 ( ( 19 ): ): 13735 - - 13738 . . DOI: 10.1103/PhysRevB.51.13735 http://doi.org/10.1103/PhysRevB.51.13735 . .
HG Gu , , , BB Pan . . A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model . . Nonl Dynam , , 2015 . . 81 ( ( 4 ): ): 2107 - - 2126 . . DOI: 10.1007/s11071-015-2129-7 http://doi.org/10.1007/s11071-015-2129-7 . .
P Hagell , , , P Piccini , , , A Björklund , , , 等 . . Dyskinesias following neural transplantation in Parkinson's disease . . Nat Neurosci , , 2002 . . 5 ( ( 7 ): ): 627 - - 628 . . DOI: 10.1038/nn863 http://doi.org/10.1038/nn863 . .
S Haghiri , , , A Ahmadi , , , M Saif . . VLSI implementable neuron-astrocyte control mechanism . . Neurocomputing , , 2016 . . 214 280 - - 296 . . DOI: 10.1016/j.neucom.2016.06.015 http://doi.org/10.1016/j.neucom.2016.06.015 . .
XJ Han , , , QS Bi , , , C Zhang , , , 等 . . Study of mixed-mode oscillations in a parametrically excited van der Pol system . . Nonl Dynam , , 2014 . . 77 ( ( 4 ): ): 1285 - - 1296 . . DOI: 10.1007/s11071-014-1377-2 http://doi.org/10.1007/s11071-014-1377-2 . .
XJ Han , , , QS Bi , , , P Ji , , , 等 . . Fast-slow analysis for para-metrically and externally excited systems with two slow rationally related excitation frequencies . . Phys Rev E , , 2015 . . 92 ( ( 1 ): ): 012911 DOI: 10.1103/PhysRevE.92.012911 http://doi.org/10.1103/PhysRevE.92.012911 . .
XJ Han , , , QS Bi , , , J Kurths . . Route to bursting via pulse-shaped explosion . . Phys Rev E , , 2018 . . 98 ( ( 1 ): ): 010201 DOI: 10.1103/PhysRevE.98.010201 http://doi.org/10.1103/PhysRevE.98.010201 . .
B Hauschildt , , , NB Janson , , , A Balanov , , , 等 . . Noise-induced cooperative dynamics and its control in coupled neuron models . . Phys Rev E , , 2006 . . 74 ( ( 5 ): ): 051906 DOI: 10.1103/PhysRevE.74.051906 http://doi.org/10.1103/PhysRevE.74.051906 . .
XY Hu , , , CX Liu . . Dynamic property analysis and circuit implementation of simplified memristive Hodgkin-Huxley neuron model . . Nonl Dynam , , 2019 . . 97 ( ( 2 ): ): 1721 - - 1733 . . DOI: 10.1007/s11071-019-05100-8 http://doi.org/10.1007/s11071-019-05100-8 . .
XY Hu , , , CX Liu , , , L Liu , , , 等 . . An electronic implementation for Morris-Lecar neuron model . . Nonl Dynam , , 2016 . . 84 ( ( 4 ): ): 2317 - - 2332 . . DOI: 10.1007/s11071-016-2647-y http://doi.org/10.1007/s11071-016-2647-y . .
B Jia , , , YC Wu , , , D He , , , 等 . . Dynamics of transitions from anti-phase to multiple in-phase synchronizations in in-hibitory coupled bursting neurons . . Nonl Dynam , , 2018 . . 93 ( ( 3 ): ): 1599 - - 1618 . . DOI: 10.1007/s11071-018-4279-x http://doi.org/10.1007/s11071-018-4279-x . .
JP Keener . . Analog circuitry for the van der Pol and FitzHugh-Nagumo equations . . IEEE Trans Syst Man Cy-bern , , 1983 . . SMC-13 ( ( 5 ): ): 1010 - - 1109 . . DOI: 10.1109/TSMC.1983.6313098 http://doi.org/10.1109/TSMC.1983.6313098 . .
IM Kyprianidis , , , V Papachristou , , , IN Stouboulos , , , 等 . . Dynamics of coupled chaotic Bonhoeffer-van der Pol oscillators . . WSEAS Trans Syst , , 2012 . . 11 ( ( 9 ): ): 516 - - 526 . . . .
ZL Liu , , , J Ma , , , G Zhang , , , 等 . . Synchronization control between two Chua's circuits via capacitive coupling . . Appl Math Comput , , 2019 . . 360 94 - - 106 . . DOI: 10.1016/j.amc.2019.05.004 http://doi.org/10.1016/j.amc.2019.05.004 . .
M Lv , , , J Ma , , , YG Yao , , , 等 . . Synchronization and wave propagation in neuronal network under field coupling . . Sci China Technol Sci , , 2019 . . 62 ( ( 3 ): ): 448 - - 457 . . DOI: 10.1007/s11431-018-9268-2 http://doi.org/10.1007/s11431-018-9268-2 . .
J Ma , , , G Zhang , , , T Hayat , , , 等 . . Model electrical activity of neuron under electric field . . Nonl Dynam , , 2019a . . 95 ( ( 2 ): ): 1585 - - 1598 . . DOI: 10.1007/s11071-018-4646-7 http://doi.org/10.1007/s11071-018-4646-7 . .
J Ma , , , ZQ Yang , , , LJ Yang , , , 等 . . A physical view of computational neurodynamics . . J Zhejiang Univ-Sci A (Appl Phys & Eng) , , 2019b . . 20 ( ( 9 ): ): 639 - - 659 . . DOI: 10.1631/jzus.A1900273 http://doi.org/10.1631/jzus.A1900273 . .
YQ Ma , , , ZR Wang , , , SY Yu , , , 等 . . A novel spiking neural network of receptive field encoding with groups of neurons decision . . Front Inform Technol Electron Eng , , 2018 . . 19 ( ( 1 ): ): 139 - - 150 . . DOI: 10.1631/FITEE.1700714 http://doi.org/10.1631/FITEE.1700714 . .
FQ Meng , , , XQ Zeng , , , ZL Wang . . Dynamical behavior and synchronization in time-delay fractional-order coupled neurons under electromagnetic radiation . . Nonl Dynam , , 2019 . . 95 ( ( 2 ): ): 1615 - - 1625 . . DOI: 10.1007/s11071-018-4648-5 http://doi.org/10.1007/s11071-018-4648-5 . .
A Mondal , , , RK Upadhyay . . Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking . . Nonl Dynam , , 2018 . . 91 ( ( 2 ): ): 1275 - - 1288 . . DOI: 10.1007/s11071-017-3944-9 http://doi.org/10.1007/s11071-017-3944-9 . .
S Mostaghimi , , , F Nazarimehr , , , S Jafari , , , 等 . . Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow . . Appl Math Comput , , 2019 . . 348 42 - - 56 . . DOI: 10.1016/j.amc.2018.11.030 http://doi.org/10.1016/j.amc.2018.11.030 . .
MV Nair , , , LK Muller , , , G Indiveri . . A differential memristive synapse circuit for on-line learning in neuromorphic computing systems . . Nano Fut , , 2017 . . 1 ( ( 3 ): ): 035003 DOI: 10.1088/2399-1984/aa954a http://doi.org/10.1088/2399-1984/aa954a . .
S Nazari , , , M Amiri , , , K Faez , , , 等 . . Multiplier-less digital implementation of neuron-astrocyte signalling on FPGA . . Neurocomputing , , 2015 . . 164 281 - - 292 . . DOI: 10.1016/j.neucom.2015.02.041 http://doi.org/10.1016/j.neucom.2015.02.041 . .
EV Pankratova , , , AI Kalyakulina , , , SV Stasenko , , , 等 . . Neuronal synchronization enhanced by neuron-astrocyte interaction . . Nonl Dynam , , 2019 . . 97 ( ( 1 ): ): 647 - - 662 . . DOI: 10.1007/s11071-019-05004-7 http://doi.org/10.1007/s11071-019-05004-7 . .
S Park , , , M Chu , , , J Kim , , , 等 . . Electronic system with memristive synapses for pattern recognition . . Sci Rep , , 2015 . . 5 ( ( 1 ): ): 10123 DOI: 10.1038/srep10123 http://doi.org/10.1038/srep10123 . .
VT Pham , , , S Jafari , , , S Vaidyanathan , , , 等 . . A novel memristive neural network with hidden attractors and its circuitry implementation . . Sci China Technol Sci , , 2016 . . 59 ( ( 3 ): ): 358 - - 363 . . DOI: 10.1007/s11431-015-5981-2 http://doi.org/10.1007/s11431-015-5981-2 . .
DE Postnov , , , RN Koreshkov , , , NA Brazhe , , , 等 . . Dy-namical patterns of calcium signaling in a functional model of neuron-astrocyte networks . . J Biol Phys , , 2009 . . 35 ( ( 4 ): ): 425 - - 445 . . DOI: 10.1007/s10867-009-9156-x http://doi.org/10.1007/s10867-009-9156-x . .
K Rajagopal , , , F Nazarimehr , , , A Karthikeyan , , , 等 . . Dy-namics of a neuron exposed to integer- and fractional-order discontinuous external magnetic flux . . Front Inform Technol Electron Eng , , 2019 . . 20 ( ( 4 ): ): 584 - - 590 . . DOI: 10.1631/FITEE.1800389 http://doi.org/10.1631/FITEE.1800389 . .
S Rakshit , , , BK Bera , , , D Ghosh , , , 等 . . Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks . . Phys Rev E , , 2018a . . 97 ( ( 5 ): ): 052304 DOI: 10.1103/PhysRevE.97.052304 http://doi.org/10.1103/PhysRevE.97.052304 . .
S Rakshit , , , BK Bera , , , D Ghosh . . Synchronization in a temporal multiplex neuronal hypernetwork . . Phys Rev E , , 2018b . . 98 ( ( 3 ): ): 032305 DOI: 10.1103/PhysRevE.98.032305 http://doi.org/10.1103/PhysRevE.98.032305 . .
S Rakshit , , , A Ray , , , BK Bera , , , 等 . . Synchronization and firing patterns of coupled Rulkov neuronal map . . Nonl Dynam , , 2018c . . 94 ( ( 2 ): ): 785 - - 805 . . DOI: 10.1007/s11071-018-4394-8 http://doi.org/10.1007/s11071-018-4394-8 . .
MJE Richardson , , , R Swarbrick . . Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise . . Phys Rev Lett , , 2010 . . 105 ( ( 17 ): ): 178102 DOI: 10.1103/PhysRevLett.105.178102 http://doi.org/10.1103/PhysRevLett.105.178102 . .
Z Rostami , , , VT Pham , , , S Jafari , , , 等 . . Taking control of initiated propagating wave in a neuronal network using magnetic radiation . . Appl Math Comput , , 2018 . . 338 141 - - 151 . . DOI: 10.1016/j.amc.2018.06.004 http://doi.org/10.1016/j.amc.2018.06.004 . .
G Seifert , , , C Steinhäuser . . Neuron-astrocyte signaling and epilepsy . . Exp Neurol , , 2013 . . 244 4 - - 10 . . DOI: 10.1016/j.expneurol.2011.08.024 http://doi.org/10.1016/j.expneurol.2011.08.024 . .
CN Takembo , , , A Mvogo , , , HPE Fouda , , , 等 . . Effect of electromagnetic radiation on the dynamics of spatio-temporal patterns in memristor-based neuronal network . . Nonl Dynam , , 2019a . . 95 ( ( 2 ): ): 1067 - - 1078 . . DOI: 10.1007/s11071-018-4616-0 http://doi.org/10.1007/s11071-018-4616-0 . .
CN Takembo , , , A Mvogo , , , HPE Fouda , , , 等 . . Wave pattern stability of neurons coupled by memristive electromagnetic induction . . Nonl Dynam , , 2019b . . 96 ( ( 2 ): ): 1083 - - 1093 . . DOI: 10.1007/s11071-019-04841-w http://doi.org/10.1007/s11071-019-04841-w . .
J Tang , , , J Zhang , , , J Ma , , , 等 . . Noise and delay sustained chimera state in small world neuronal network . . Sci China Technol Sci , , 2019 . . 62 ( ( 7 ): ): 1134 - - 1140 . . DOI: 10.1007/s11431-017-9282-x http://doi.org/10.1007/s11431-017-9282-x . .
RK Upadhyay , , , A Mondal , , , WW Teka . . Mixed mode oscillations and synchronous activity in noise induced modified Morris-Lecar neural system . . Int J Bifurc Chaos , , 2017 . . 27 ( ( 5 ): ): 1730019 DOI: 10.1142/S0218127417300191 http://doi.org/10.1142/S0218127417300191 . .
R Uzun , , , E Yilmaz , , , M Ozer . . Effects of autapse and ion channel block on the collective firing activity of Newman-Watts small-world neuronal networks . . Phys A , , 2017 . . 486 386 - - 396 . . DOI: 10.1016/j.physa.2017.05.049 http://doi.org/10.1016/j.physa.2017.05.049 . .
CN Wang , , , M Lv , , , A Alsaedi , , , 等 . . Synchronization stability and pattern selection in a memristive neuronal network . . Chaos , , 2017 . . 27 ( ( 11 ): ): 113108 DOI: 10.1063/1.5004234 http://doi.org/10.1063/1.5004234 . .
YH Wang , , , XY Xu , , , YT Zhu , , , 等 . . Neural energy mechanism and neurodynamics of memory transformation . . Nonl Dynam , , 2019 . . 97 ( ( 1 ): ): 697 - - 714 . . DOI: 10.1007/s11071-019-05007-4 http://doi.org/10.1007/s11071-019-05007-4 . .
FQ Wu , , , CN Wang , , , Y Xu , , , 等 . . Model of electrical activity in cardiac tissue under electromagnetic induction . . Sci Rep , , 2016 . . 6 ( ( 1 ): ): 28 DOI: 10.1038/s41598-016-0031-2 http://doi.org/10.1038/s41598-016-0031-2 . .
FQ Wu , , , CN Wang , , , WY Jin , , , 等 . . Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise . . Phys A , , 2017 . . 469 81 - - 88 . . DOI: 10.1016/j.physa.2016.11.056 http://doi.org/10.1016/j.physa.2016.11.056 . .
FQ Wu , , , J Ma , , , G Zhang . . A new neuron model under electromagnetic field . . Appl Math Comput , , 2019 . . 347 590 - - 599 . . DOI: 10.1016/j.amc.2018.10.087 http://doi.org/10.1016/j.amc.2018.10.087 . .
F Xu , , , JQ Zhang , , , TT Fang , , , 等 . . Synchronous dynamics in neural system coupled with memristive synapse . . Nonl Dynam , , 2018 . . 92 ( ( 3 ): ): 1395 - - 1402 . . DOI: 10.1007/s11071-018-4134-0 http://doi.org/10.1007/s11071-018-4134-0 . .
Q Xu , , , QL Zhang , , , H Qian , , , 等 . . Crisis-induced coexisting multiple attractors in a second-order nonautonomous memristive diode bridge-based circuit . . Int J Circ Theor Appl , , 2018 . . 46 ( ( 10 ): ): 1917 - - 1927 . . DOI: 10.1002/cta.2492 http://doi.org/10.1002/cta.2492 . .
Y Xu , , , Y Jia , , , J Ma , , , 等 . . Collective responses in electrical activities of neurons under field coupling . . Sci Rep , , 2018a . . 8 ( ( 1 ): ): 1349 DOI: 10.1038/s41598-018-19858-1 http://doi.org/10.1038/s41598-018-19858-1 . .
Y Xu , , , Y Jia , , , MY Ge , , , 等 . . Effects of ion channel blocks on electrical activity of stochastic Hodgkin-Huxley neural network under electromagnetic induction . . Neurocomputing , , 2018b . . 283 196 - - 204 . . DOI: 10.1016/j.neucom.2017.12.036 http://doi.org/10.1016/j.neucom.2017.12.036 . .
Y Xu , , , Y Jia , , , HW Wang , , , 等 . . Spiking activities in chain neural network driven by channel noise with field coupling . . Nonl Dynam , , 2019 . . 95 ( ( 4 ): ): 3237 - - 3247 . . DOI: 10.1007/s11071-018-04752-2 http://doi.org/10.1007/s11071-018-04752-2 . .
Z Yao , , , J Ma , , , YG Yao , , , 等 . . Synchronization realization between two nonlinear circuits via an induction coil coupling . . Nonl Dynam , , 2019 . . 96 ( ( 1 ): ): 205 - - 217 . . DOI: 10.1007/s11071-019-04784-2 http://doi.org/10.1007/s11071-019-04784-2 . .
WJ Ye , , , WD Mai , , , GW Hu . . Effects of the electromagnetic radiation on cognitive performance: a model study . . Nonl Dynam , , 2018 . . 93 ( ( 4 ): ): 2473 - - 2485 . . DOI: 10.1007/s11071-018-4337-4 http://doi.org/10.1007/s11071-018-4337-4 . .
DS Yu , , , CY Zheng , , , HHC Iu , , , 等 . . A new circuit for emulating memristors using inductive coupling . . IEEE Access , , 2017 . . 5 1284 - - 1295 . . DOI: 10.1109/ACCESS.2017.2649573 http://doi.org/10.1109/ACCESS.2017.2649573 . .
Y Yu , , , C Zhang , , , XJ Han . . Routes to bursting in active control system with multiple time delays . . Nonl Dynam , , 2017 . . 88 ( ( 3 ): ): 2241 - - 2254 . . DOI: 10.1007/s11071-017-3373-9 http://doi.org/10.1007/s11071-017-3373-9 . .
YZ Zhang , , , Z Liu , , , HG Wu , , , 等 . . Dimensionality re-duction analysis for detecting initial effects on synchro-nization of memristor-coupled system . . IEEE Access , , 2019a . . 7 109689 - - 109698 . . DOI: 10.1109/ACCESS.2019.2933252 http://doi.org/10.1109/ACCESS.2019.2933252 . .
YZ Zhang , , , Z Liu , , , HG Wu , , , 等 . . Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis . . Chaos Sol Fract , , 2019b . . 127 354 - - 363 . . DOI: 10.1016/j.chaos.2019.07.004 http://doi.org/10.1016/j.chaos.2019.07.004 . .
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